A Study of Dynamic Instability for Sigmoid Functionally Graded Material Plates on Elastic Foundation

Han Sung-Cheon; Park Weon-Tae

doi:10.7734/COSEIK.2015.28.1.85

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2015 Vol.28, Issue 1 Preview Page Next Page

A Study of Dynamic Instability for Sigmoid Functionally Graded Material Plates on Elastic Foundation 탄성지반위에 놓인 S형상 점진기능재료(FGM)판의동적 불안정성에 관한 연구

2015. pp. 85-92

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Abstract

탄성지반위에 놓인 S형상 점진기능재료 고차전단변형 판의 동적 불안정성에 대하여 연구하였다. 고차전단변형이론은 점진기능재료 판의 두께방향으로의 전단변형률과 전단응력의 곡선변화 효과를 고려할 수 있다. Mathieu-Hill 방정식의 형태로 유도된 지배방정식에서 Bolotin 방법을 이용하여 동적 불안정 영역을 결정하였다. 동적 불안정 영역의 경계는 동적 하중과 여기진동수와의 관계로 나타내었다. 고차전단변형이론과 탄성지반 효과가 S형상 점진기능재료 판의 동적 불안정성에 미치는 효과를 제시하였다. Winkler와 Pasternak탄성지반 매개변수의 관계를 수치해석 결과를 통하여 고찰하였다. 또한 정적 하중계수, 거듭제곱 지수 그리고 폭-두께비 등의 동적 불안정 영역에 대한 영향을 분석하였다. 본 연구의 결과를 검증하기 위해 참고문헌의 결과와 비교 분석하였다. 본 연구에서 제시한 이론적 발전과 수치결과들은 S형상 점진기능재료 구조물의 동적 불안정 해석을 위한 참고자료로 활용될 수 있을 것이다.

This article presents the dynamic instability response of sigmoid functionally graded material plates on elastic foundation using the higher-order shear deformation theory. The higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The governing equations are then written in the form of Mathieu?Hill equations and then Bolotin’s method is employed to determine the instability regions. The boundaries of the instability regions are represented in the dynamic load and excitation frequency plane. The results of dynamic instability analysis of sigmoid functionally graded material plate are presented using the Navier’s procedure to illustrate the effect of elastic foundation parameter on dynamic response. The relations between Winkler and Pasternak elastic foundation parameter are discussed by numerical results. Also, the effects of static load factor, power-law index and side-to-thickness ratio on dynamic instability analysis are investigated and discussed. In order to validate the present solutions, the reference solutions are used and discussed. The theoretical development as well as numerical solutions presented herein should serve as reference for the dynamic instability study of S-FGM plates.

키워드

동적 불안정, 고차전단변형이론, Pasternak 탄성지반, S형상 점진기능재료 판

dynamic instability; higher-order shear deformation theory; pasternak elastic foundation; sigmoid functionally graded material(S-FGM) plate

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Information

Publisher :Computational Structural Engineering Institute of Korea
Publisher(Ko) :한국전산구조공학회
Journal Title :Journal of the Computational Structural Engineering Institute of Korea
Journal Title(Ko) :한국전산구조공학회 논문집
Volume : 28
No :1
Pages :85-92
Received Date : 2014-11-12
Revised Date : 2014-11-22
Accepted Date : 2014-11-24
DOI :https://doi.org/10.7734/COSEIK.2015.28.1.85

Journal of the Computational Structural Engineering Institute of Korea ISSN:1229-3059(Print) 2287-2302(Online) 한국전산구조공학회 논문집

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